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An improved certificateless strong key-insulated signature scheme in the standard model
Some new results on cross correlation of $p$-ary $m$-sequence and its decimated sequence
1. | School of Mathemetics & Computation Science, Anqing Normal University, Anqing, Anhui 246133, China |
2. | Department of Mathematic and Statistics, Centtal China Normal University, Wuhan, Hubei 430079, China |
3. | Department of Mathematic Sciences, Yangzhou University, Yangzhou, Jiangsu 225002, China, China |
References:
[1] |
A. W. Bluher, On $x^{q+1}+ax+b$, Finite Fields Appl., 10 (2004), 285-305.
doi: 10.1016/j.ffa.2003.08.004. |
[2] |
W. Chen, J. Luo and Y. Tang, Exponential sums from half quadratic forms and its applications, in Proc. ISIT'14, 2014, 3145-3149. |
[3] |
S. T. Choi, J. S. No and H. Chung, On the cross-correlation of a ternary m-sequence of period $3^{4k+2}-1$ and its decimated sequence by $(3^{2k+1}+1)^{2}$ over 8, in Proc. ISIT'10, 2010, 1268-1271. |
[4] |
S. T. Choi, J. S. No and H. Chung, On the cross-correlation of a $p$-ary m-sequence of period $p^{2m}-1$ and its decimated sequence by $\frac{(p^m+1)^2}{2(p+1)}$, IEEE Trans. Inf. Theory, 58 (2012), 1873-1879.
doi: 10.1109/TIT.2011.2177573. |
[5] |
H. Dobbertin, P. Felke and T. Helleseth, Niho type cross correlation functions via Dickson polynomials and Kloosterman sums, IEEE Trans. Inf. Theory, 52 (2006), 613-627.
doi: 10.1109/TIT.2005.862094. |
[6] |
T. Helleseth, Some results about the cross-correlation function between two maximal-linear sequence, Discrete Math., 16 (1976), 209-232. |
[7] |
R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Boston, 1983. |
[8] |
J. Luo and K. Feng, On the weight distribution of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 5332-5344.
doi: 10.1109/TIT.2008.2006424. |
[9] |
J. Luo and K. Feng, Cyclic codes and sequences from generalized Coulter-Matthews function, IEEE Trans. Inf. Theory, 54 (2008), 5345-5353.
doi: 10.1109/TIT.2008.2006394. |
[10] |
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with six-valued cross correlation, in Proc. IWSDA'11, 2011, 44-47. |
[11] |
J, Luo, Y. Tang and H. Wang, Exponential sums, cyclic codes and sequences: the odd characteristic Kasami case,, preprint, ().
|
[12] |
G. J. Ness, T. Helleseth and A. Kholosha, On the correlation distribution of the Coulter-Matthews decimation, IEEE Trans. Inf. Theory, 52 (2006), 2241-2247.
doi: 10.1109/TIT.2006.872857. |
[13] |
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Cross-correlation distribution of p-ary m-sequence of period $p^{4k}-1$ and its decimated sequences by $(\frac{p^{2k}+1}{2})^{2}$, IEEE Trans. Inf. Theory, 54 (2008),3140-3149.
doi: 10.1109/TIT.2008.924694. |
[14] |
Y. Sun, Z. Wang, H. Li and T. Yan, The cross-correlation distribution of a $p$-ary m-sequence of period $p^{2k}-1$ and its decimated sequence by $\frac{(p^k+1)^2}{2(p^e+1)}$, Adv. Math. Commun., 7 (2013), 409-424.
doi: 10.3934/amc.2013.7.409. |
[15] |
Y. Xia, C. Li, X. Zeng and T. Helleseth, Some results on cross-correlation distribution between a $p$-ary $m$-sequence and its decimated sequences, IEEE Trans. Inf. Theory, 60 (2014), 7368-7381.
doi: 10.1109/TIT.2014.2350775. |
show all references
References:
[1] |
A. W. Bluher, On $x^{q+1}+ax+b$, Finite Fields Appl., 10 (2004), 285-305.
doi: 10.1016/j.ffa.2003.08.004. |
[2] |
W. Chen, J. Luo and Y. Tang, Exponential sums from half quadratic forms and its applications, in Proc. ISIT'14, 2014, 3145-3149. |
[3] |
S. T. Choi, J. S. No and H. Chung, On the cross-correlation of a ternary m-sequence of period $3^{4k+2}-1$ and its decimated sequence by $(3^{2k+1}+1)^{2}$ over 8, in Proc. ISIT'10, 2010, 1268-1271. |
[4] |
S. T. Choi, J. S. No and H. Chung, On the cross-correlation of a $p$-ary m-sequence of period $p^{2m}-1$ and its decimated sequence by $\frac{(p^m+1)^2}{2(p+1)}$, IEEE Trans. Inf. Theory, 58 (2012), 1873-1879.
doi: 10.1109/TIT.2011.2177573. |
[5] |
H. Dobbertin, P. Felke and T. Helleseth, Niho type cross correlation functions via Dickson polynomials and Kloosterman sums, IEEE Trans. Inf. Theory, 52 (2006), 613-627.
doi: 10.1109/TIT.2005.862094. |
[6] |
T. Helleseth, Some results about the cross-correlation function between two maximal-linear sequence, Discrete Math., 16 (1976), 209-232. |
[7] |
R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Boston, 1983. |
[8] |
J. Luo and K. Feng, On the weight distribution of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 5332-5344.
doi: 10.1109/TIT.2008.2006424. |
[9] |
J. Luo and K. Feng, Cyclic codes and sequences from generalized Coulter-Matthews function, IEEE Trans. Inf. Theory, 54 (2008), 5345-5353.
doi: 10.1109/TIT.2008.2006394. |
[10] |
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with six-valued cross correlation, in Proc. IWSDA'11, 2011, 44-47. |
[11] |
J, Luo, Y. Tang and H. Wang, Exponential sums, cyclic codes and sequences: the odd characteristic Kasami case,, preprint, ().
|
[12] |
G. J. Ness, T. Helleseth and A. Kholosha, On the correlation distribution of the Coulter-Matthews decimation, IEEE Trans. Inf. Theory, 52 (2006), 2241-2247.
doi: 10.1109/TIT.2006.872857. |
[13] |
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Cross-correlation distribution of p-ary m-sequence of period $p^{4k}-1$ and its decimated sequences by $(\frac{p^{2k}+1}{2})^{2}$, IEEE Trans. Inf. Theory, 54 (2008),3140-3149.
doi: 10.1109/TIT.2008.924694. |
[14] |
Y. Sun, Z. Wang, H. Li and T. Yan, The cross-correlation distribution of a $p$-ary m-sequence of period $p^{2k}-1$ and its decimated sequence by $\frac{(p^k+1)^2}{2(p^e+1)}$, Adv. Math. Commun., 7 (2013), 409-424.
doi: 10.3934/amc.2013.7.409. |
[15] |
Y. Xia, C. Li, X. Zeng and T. Helleseth, Some results on cross-correlation distribution between a $p$-ary $m$-sequence and its decimated sequences, IEEE Trans. Inf. Theory, 60 (2014), 7368-7381.
doi: 10.1109/TIT.2014.2350775. |
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